Important Formulas - Area - Tricks & Shortcuts

1. Results on Trianglesi. Sum of the angles of a triangle is 180°.
ii. The sum of any two sides of a triangle is greater than the third side.
iii. Pythagoras Theorem: In a right-angled
triangle, (Hypotenuse)2 = (Base)2 + (Height)2.

iv. The line joining the mid-point of a side of a triangle to the positive
vertex is called the median.
v. The point where the three medians of a triangle meet, is called centroid. The
centroid divided each of the medians in the ratio 2 : 1
vi. In an isosceles triangle, the altitude from
the vertex bisects the base.
vii. The median of a triangle divides it into two triangles of the same area.
viii. The area of the triangle formed by joining the mid-points of the sides of
a given triangle is one-fourth of the area of the given triangle.

2. Results on Quadrilateralsi. The diagonals of a parallelogram
bisect each other.
ii. Each diagonal of a parallelogram divides it into triangles of the same
area.
iii. The diagonals of a rectangle are equal and bisect each other.
iv. The diagonals of a square are equal and bisect each other at right angles.
v. The diagonals of a rhombus are unequal and bisect each other at right
angles.
vi. A parallelogram and a rectangle on the same base and between the same
parallels are equal in area.
vii. Of all the parallelogram of given sides, the parallelogram which is a
rectangle has the greatest area.

Important Formulas1. Area of rectangle = (Length x Breadth)

Therefore length=(Area/Breadth) and
Breadth = (Area/Length)

2. Perimeter of a rectangle = 2(Length + Breadth).

3. Area of a square = (side)2 = (1/2)(diagonal)2

4. Area of 4 walls of a room = 2 (Length
+ Breadth) x Height.

5. Area of a triangle
= (1/2)x Base x Height

6. Area of a triangle = √s(s-a)(s-b)(s-c) (square root of s(s-a)(s-b)(s-c)
)

7. Area of an equilateral triangle =(√3/4) x
(side)2.
8. Radius of incircle of an equilateral
triangle of side a = (a/(2√3))

9. Radius of circumcircle of an equilateral triangle of side a = a/√3

10. Radius of incircle of a triangle of area
Δ and semi-perimeter s = Δ/s

11. Area of parallelogram =
(Base x Height)

12. Area of a rhombus = ½ x (Product of diagonals)

13. Area of a trapezium = ½ x (sum of parallel sides) x
distance between them